8. Identify the percent of change from \( \frac{2}{5} \) to \( \frac{5}{15} \) as an increase or a decrease. Then fir percent of change. Round to the nearest tenth of a percent.

To find the percent of change from \( \frac{2}{5} \) to \( \frac{5}{15} \), we first need to calculate the difference between the two values and then divide by the original value to find the percent change. Given: Original value = \( \frac{2}{5} \) New value = \( \frac{5}{15} \) 1. Calculate the difference between the new value and the original value: \[ \text{Difference} = \frac{5}{15} - \frac{2}{5} \] 2. Calculate the percent change: \[ \text{Percent change} = \left( \frac{\text{Difference}}{\text{Original value}} \right) \times 100\% \] Let's calculate the percent change. Calculate the value by following steps: - step0: Calculate: \(\frac{5}{15}-\frac{2}{5}\) - step1: Reduce the fraction: \(\frac{1}{3}-\frac{2}{5}\) - step2: Reduce fractions to a common denominator: \(\frac{5}{3\times 5}-\frac{2\times 3}{5\times 3}\) - step3: Multiply the numbers: \(\frac{5}{15}-\frac{2\times 3}{5\times 3}\) - step4: Multiply the numbers: \(\frac{5}{15}-\frac{2\times 3}{15}\) - step5: Transform the expression: \(\frac{5-2\times 3}{15}\) - step6: Multiply the numbers: \(\frac{5-6}{15}\) - step7: Subtract the numbers: \(\frac{-1}{15}\) - step8: Rewrite the fraction: \(-\frac{1}{15}\) The difference between the new value and the original value is \( -\frac{1}{15} \) or approximately -0.0667. Now, let's calculate the percent change: \[ \text{Percent change} = \left( \frac{-\frac{1}{15}}{\frac{2}{5}} \right) \times 100\% \] \[ \text{Percent change} = \left( \frac{-\frac{1}{15}}{\frac{2}{5}} \right) \times 100\% = \left( \frac{-1}{15} \times \frac{5}{2} \right) \times 100\% \] \[ \text{Percent change} = \left( \frac{-5}{30} \right) \times 100\% = \left( \frac{-1}{6} \right) \times 100\% \] \[ \text{Percent change} = -16.67\% \] Therefore, the percent of change from \( \frac{2}{5} \) to \( \frac{5}{15} \) is a decrease of 16.67%.